Ana Achucarro, Julian Borrill & Andrew Liddle
Semilocal strings are `worms' of energy that arise from a
complex interaction of quantum matter and force fields during a phase transition.
This can be in a condensed matter system - such as superfluid helium -
or in the very early universe, during the fracturing of a unified force
into its constituents. The
result is a line-like region of space in which the phase transition has
been prevented from occuring by a combination of the topology of the vacuum
and the energetics of the quantum system.
The strings originate as open segments, with a north magnetic
monopole on one end and a south monopole on the other. As with any magnet,
like poles repel and unlike poles attract. When two oppositely-oriented
ends meet the monopoles annihilate forming either a closed loop (if the
ends belong to the same string) or a longer segment (if the ends belong
to different strings). In the first case the string loops shrink under
their own tension and rapidly disappear. In the second case, however, the
strings build up into longer and longer objects, ultimately spanning the
universe. This question of the disappearance or persistence of the strings
motivated our simulations.
If semilocal strings do persist then they would be a possible
source of the primordial density perturbations needed to seed the formation
of the gravitationally bound astronomical objects we observe today - from
planets to clusters and superclusters of galaxies. In certain models they
would also provide a mechanism for baryogenesis, generating the slight
asymmetry between matter and antimatter in the early universe that allows
us to exist today.
Semilocal String Formation In 2 Dimensions
We began by investigating the behaviour of the strings in
2 dimensions, with the string axis forced to lie perpendicular to the simulation
plane. The following images are of semilocal string formation
on a periodic square lattice, and show the magnetic flux energy density
over the simulation plane.
A paper discussing these simulations, published in Physical
Review, is available on the archive as hep-ph/9702368
An mpg animation (400 Kb) of semilocal string formation in
2 dimensions is here
Semilocal String Formation In 3 Dimensions
Using the Cray T3E supercomputer at the National Energy Research
Scientific Computing Center (NERSC)
we were able to perform full 3 dimensional simulations. The following images
are of semilocal string formation on a periodic cubic lattice with 256
points on each side. They show isosurfaces of the flux energy density measured
as a fraction of the theoretical peak value. Particular thanks are due
to Kevin Campbell and Terry Ligocki of the NERSC Visualisation
Group for all their help.
The simulation in close up (t = 20 - 100, isosurface = 1/4)
stereo (50 Kb jpg).
The full simulation volume (t = 20 - 100, isosurface = 1/4)
(100 Kb jpg).
Note that for the red-blue stereo images the red lens should
be over your left eye. Stereo quality will depend heavily on the accuracy
of your colour mapping.
Initial evolution (t = 1 - 20, isosurface = 1/32) : normal
stereo (0.5 Mb mpg).
Segment growth by connection (t = 20 - 200, isosurface =
1/4) : normal
stereo (4.2 Mb mpg).
Loop production and decay (t = 20 - 200, isosurface = 1/4)
stereo (4.7 Mb mpg).
Tracking back through the simulation (t = 20 - 200, isosurface
= 1/4) : normal
stereo (3.5 Mb mpg).
The full simulation volume (t = 20 - 2000, isosurface = 1/2)
(6.8 Mb mpg).
Alternatively, rather than plotting an isosurface, we
can use colour and opacity as measures of the flux density, which helps
to conveys the physically correct notion of the semilocal strings condensing
out of an initial low-level background flux.
Three papers discussing these simulations have
been published, in Physical Review Letters, (hep-ph/9802306), in
Physica B (hep-ph/9810459), and
in ``Particles, Strings and Cosmology - PASCOS-98'', editor P. Nath,
World Scientific 1999 (available here)
This work has also been the subject of
online articles by ABC
Lab (also carried by the University
of California and UniSci online),
Daily Cal and the
Bronx High School of Science, and print-only articles by Science
News [Volume 154, October 1998] , Scientific Computing World [Issue
41, September 1998] , Science
et Vie [Number 977, February 1999] and Konr@d
[June/July 1999] .